Tikhonov regularization with ℓ0-term complementing a~convex penalty: ℓ1-convergence under sparsity constraints
نویسندگان
چکیده
منابع مشابه
Convergence rates for regularization with sparsity constraints
Tikhonov regularization with p-powers of the weighted `p norms as penalties, with p ∈ (1, 2), have been lately employed in reconstruction of sparse solutions of ill-posed inverse problems. This paper points out convergence rates for such a regularization with respect to the norm of the weighted spaces, by assuming that the solutions satisfy certain smoothness (source) condition. The meaning of ...
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This paper addresses the regularization by sparsity constraints by means of weighted lp penalties for 0 ≤ p ≤ 2. For 1 ≤ p ≤ 2 special attention is payed to convergence rates in norm and to source conditions. As main results it is proven that one gets a convergence rate of √ δ in the 2-norm for 1 < p ≤ 2 and in the 1-norm for p = 1 as soon as the unknown solution is sparse. The case p = 1 needs...
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ژورنال
عنوان ژورنال: Journal of Inverse and Ill-posed Problems
سال: 2019
ISSN: 0928-0219,1569-3945
DOI: 10.1515/jiip-2019-0008